/* "Reanalyzing the Link between Democracy and Economic Development"*/
/* journal: International Area Studies Review
/* authors: "Pelke, Lars"*/
/* date: 2023-07-24*/
/* written under "Stata version 17  MP—Parallel Edition"*/

/**********************/
/*Clean and set memory*/
/**********************/
clear all
set matsize 5000
set more off

/******************/
/*Install programs*/
/******************/
cap ssc install xtabond2 
cap ssc install xtivreg2 
cap ssc install spmat 
cap ssc install spmack

/*********************/
/*Sets base directory*/
/*********************/
cd ""      										    /* Set base directory                         */
global limit=25                                                                             /* Evaluate effects 25 years after transition */
local repsBS=100                                                                            /* Number of bootstrap repetitions            */


/* Load data */

use "data/vdem_data.dta"

/* XTset */

xtset country_id year

/* Generate y-variable for GDP per capita */

gen y = gdppc_ppp_bcbt_mean_log*100

gen id = country_id


/*******************************************************************************************************************************/
/*******************************************************************************************************************************/
/*********************DEFINE REQUIRED PROGRAMS THAT WILL BE USED DURING THE EXECUTION OF THIS DO FILE **************************/
/*******************************************************************************************************************************/
/*******************************************************************************************************************************/

capture program drop vareffects
program define vareffects, eclass

quietly: nlcom (effect1: _b[shortrun]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  , post

quietly: nlcom (effect2: _b[effect1]*_b[lag1]+_b[shortrun]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  , post

quietly: nlcom (effect3: _b[effect2]*_b[lag1]+_b[effect1]*_b[lag2]+_b[shortrun]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  , post
	  
quietly: nlcom (effect4: _b[effect3]*_b[lag1]+_b[effect2]*_b[lag2]+_b[effect1]*_b[lag3]+_b[shortrun]) ///
	  (effect3: _b[effect3]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  , post	  

forvalues j=5(1)$limit{	  
local j1=`j'-1
local j2=`j'-2
local j3=`j'-3
local j4=`j'-4

quietly: nlcom (effect`j': _b[effect`j1']*_b[lag1]+_b[effect`j2']*_b[lag2]+_b[effect`j3']*_b[lag3]+_b[effect`j4']*_b[lag4]+_b[shortrun]) ///
	  (effect`j1': _b[effect`j1']) ///
	  (effect`j2': _b[effect`j2']) ///
	  (effect`j3': _b[effect`j3']) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  , post	  	  

}

quietly: nlcom (effect$limit: _b[effect$limit]) ///
	  (longrun: _b[shortrun]/(1-_b[lag1]-_b[lag2]-_b[lag3]-_b[lag4])) ///
      (shortrun: _b[shortrun]) ///
	  (persistence: _b[lag1]+_b[lag2]+_b[lag3]+_b[lag4]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  , post
ereturn display
end


capture program drop vareffects8
program define vareffects8, eclass

quietly: nlcom (effect1: _b[shortrun]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post

quietly: nlcom (effect2: _b[effect1]*_b[lag1]+_b[shortrun]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post

quietly: nlcom (effect3: _b[effect2]*_b[lag1]+_b[effect1]*_b[lag2]+_b[shortrun]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post
	  
quietly: nlcom (effect4: _b[effect3]*_b[lag1]+_b[effect2]*_b[lag2]+_b[effect1]*_b[lag3]+_b[shortrun]) ///
	  (effect3: _b[effect3]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post
	  
quietly: nlcom (effect5: _b[effect4]*_b[lag1]+_b[effect3]*_b[lag2]+_b[effect2]*_b[lag3]+_b[effect1]*_b[lag4]+_b[shortrun]) ///
	  (effect4: _b[effect4]) ///
	  (effect3: _b[effect3]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post
	  
quietly: nlcom (effect6: _b[effect5]*_b[lag1]+_b[effect4]*_b[lag2]+_b[effect3]*_b[lag3]+_b[effect2]*_b[lag4]+_b[effect1]*_b[lag5]+_b[shortrun]) ///
	  (effect5: _b[effect5]) ///
	  (effect4: _b[effect4]) ///
	  (effect3: _b[effect3]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post	

quietly: nlcom (effect7: _b[effect6]*_b[lag1]+_b[effect5]*_b[lag2]+_b[effect4]*_b[lag3]+_b[effect3]*_b[lag4]+_b[effect2]*_b[lag5]+_b[effect1]*_b[lag6]+_b[shortrun]) ///
	  (effect6: _b[effect6]) ///
	  (effect5: _b[effect5]) ///
	  (effect4: _b[effect4]) ///
	  (effect3: _b[effect3]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post	

quietly: nlcom (effect8: _b[effect7]*_b[lag1]+_b[effect6]*_b[lag2]+_b[effect5]*_b[lag3]+_b[effect4]*_b[lag4]+_b[effect3]*_b[lag5]+_b[effect2]*_b[lag6]+_b[effect1]*_b[lag7]+_b[shortrun]) ///
	  (effect7: _b[effect7]) ///
	  (effect6: _b[effect6]) ///
	  (effect5: _b[effect5]) ///
	  (effect4: _b[effect4]) ///
	  (effect3: _b[effect3]) ///
	  (effect2: _b[effect2]) ///
	  (effect1: _b[effect1]) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post	
	  
	  
forvalues j=9(1)$limit{	  
local j1=`j'-1
local j2=`j'-2
local j3=`j'-3
local j4=`j'-4
local j5=`j'-5
local j6=`j'-6
local j7=`j'-7
local j8=`j'-8

quietly: nlcom (effect`j': _b[effect`j1']*_b[lag1]+_b[effect`j2']*_b[lag2]+_b[effect`j3']*_b[lag3]+_b[effect`j4']*_b[lag4]+_b[effect`j5']*_b[lag5]+_b[effect`j6']*_b[lag6]+_b[effect`j7']*_b[lag7]+_b[effect`j8']*_b[lag8]+_b[shortrun]) ///
	  (effect`j1': _b[effect`j1']) ///
	  (effect`j2': _b[effect`j2']) ///
	  (effect`j3': _b[effect`j3']) ///
	  (effect`j4': _b[effect`j4']) ///
	  (effect`j5': _b[effect`j5']) ///
	  (effect`j6': _b[effect`j6']) ///
	  (effect`j7': _b[effect`j7']) ///
	  (shortrun: _b[shortrun]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post	  	  

}

quietly: nlcom (effect$limit: _b[effect$limit]) ///
	  (longrun: _b[shortrun]/(1-_b[lag1]-_b[lag2]-_b[lag3]-_b[lag4]-_b[lag5]-_b[lag6]-_b[lag7]-_b[lag8])) ///
      (shortrun: _b[shortrun]) ///
	  (persistence: _b[lag1]+_b[lag2]+_b[lag3]+_b[lag4]+_b[lag5]+_b[lag6]+_b[lag7]+_b[lag8]) ///
	  (lag1: _b[lag1]) ///
	  (lag2: _b[lag2]) ///
	  (lag3: _b[lag3]) ///
	  (lag4: _b[lag4]) ///
	  (lag5: _b[lag5]) ///
	  (lag6: _b[lag6]) ///
	  (lag7: _b[lag7]) ///
	  (lag8: _b[lag8]) ///
	  , post
ereturn display
end


capture program drop helm
program define helm
*
* This program will do Helmert transformation for a list of variables
* NOTE:  must have variables named id, year   
* to use enter >> helm var1 var2...
* new variables will be names with h_ in front h_var1  and so on
*
qui while "`1'"~="" {
gsort id -year                /*sort years descending */
tempvar one sum n m w 
* capture drop h_`1'         /* IF the variable exist - it will remain and not generated again */
gen `one'=1 if `1'~=.             /*generate one if x is nonmissing */
qui by id: gen `sum'=sum(`1')-`1' /*running sum without current element */
qui by id: gen `n'=sum(`one')-1     /*number of obs included in the sum */
replace `n'=. if `n'<=0             /* n=0 for last observation and =-1 if
                                   last observation is missing*/
gen `m'=`sum'/`n'                 /* m is forward mean of variable x*/
gen `w'=sqrt(`n'/(`n'+1))         /* weight on mean difference */
capture gen h_`1'=`w'*(`1'-`m')             /* transformed variable */ 
sort id year
mac shift
}
end




capture program hhkBS, eclass
syntax anything[, ydeep(integer 1896) ystart(integer 1900) yfinal(integer 2019) truncate(integer 4) depvarlags(integer 4)]
	local 0 `anything' 
	gettoken yvar 0 : 0 /*dependent variable*/
	gettoken seqexg   0 : 0, match(par) /*Sequentially exogenous variables*/
	gettoken gmminst  0 : 0, match(par) /*gmm style instruments*/
	gettoken gmmtrunc 0 : 0, match(par) /*gmm style instruments, truncated*/
	gettoken excov 0 : 0, match(par) /*exogenous covariates: diff coefficient for each equation*/
		
/*declares panel structure and defines estimation sample*/
quietly: tsset, clear
quietly: tsset newcl year
sort newcl year
quietly: xtreg `yvar' `seqexg' `excov', fe
quietly: gen tsample=e(sample)

/**************************************************************************************
*********Helmert transformations and partialing out covariates************************/
quietly: gen id=newcl
sort newcl year
quietly: reg `yvar' `excov' if tsample==1
quietly: predict `yvar'_res if tsample==1, resid
quietly: helm `yvar'_res
rename h_`yvar'_res h_`yvar'
drop `yvar'_res

local num_seqexg=0
local seqexg_helm
foreach var of local seqexg{
sort newcl year
local num_seqexg=`num_seqexg'+1
quietly: gen seqexg`num_seqexg'=`var'
quietly: reg seqexg`num_seqexg' `excov' if tsample==1
quietly: predict seqexg`num_seqexg'_res if tsample==1, resid
quietly: helm seqexg`num_seqexg'_res
rename h_seqexg`num_seqexg'_res h_seqexg`num_seqexg'
local seqexg_helm `seqexg_helm' h_seqexg`num_seqexg'
drop seqexg`num_seqexg' seqexg`num_seqexg'_res
}

/***************************************************************
***************Creation of GMM instruments**********************
***************************************************************/
local gmmlist
local num_gmm=0
foreach var of local gmminst{
sort newcl year
local num_gmm=`num_gmm'+1
quietly: gen abond`num_gmm'=`var'
quietly: reg abond`num_gmm' `excov' if tsample==1
quietly: predict abond`num_gmm'_res, resid
drop abond`num_gmm' 
rename abond`num_gmm'_res abond`num_gmm'

quietly: replace abond`num_gmm'=0 if abond`num_gmm'==.
local gmmlist `gmmlist' abond`num_gmm' 

}

local gmmlist_trunc
local num_gmm_trunc=0
foreach var of local gmmtrunc{
sort newcl year
local num_gmm_trunc=`num_gmm_trunc'+1
quietly: gen abond_trunc`num_gmm_trunc'=`var'
quietly: reg abond_trunc`num_gmm_trunc' `excov' if tsample==1
quietly: predict abond_trunc`num_gmm_trunc'_res, resid
drop abond_trunc`num_gmm_trunc' 
rename abond_trunc`num_gmm_trunc'_res abond_trunc`num_gmm_trunc'
quietly: replace abond_trunc`num_gmm_trunc'=0 if abond_trunc`num_gmm_trunc'==.
local gmmlist_trunc `gmmlist_trunc' abond_trunc`num_gmm_trunc' 
}

/***************************************************************
***************Estimator  for year j between maxy and  start***/
***************************************************************/
sort newcl year

*initialize objects*
local obs=0
quietly: gen samptemp=.
matrix def Num1=J(`num_seqexg', 1, 0)
matrix def Num2=J(`num_seqexg', `num_seqexg', 0) 
matrix def Den1=J(`num_seqexg', `num_seqexg', 0) 

forvalues maxyear=`ystart'(1)`yfinal'{

local maxinst=`maxyear'-`ydeep' /*deeper gmm lags until ydeep. Warning: many of these instruments may be zero if no data*/
local maxtrunc=min(`truncate',`maxinst')
local j=`maxyear'-1960+1

*ivreg to check for collinearities and obtain degree of overidentification*
cap ivreg2 h_`yvar' (`seqexg_helm'=l(1/`maxinst').(`gmmlist') l(1/`maxtrunc').(`gmmlist_trunc'))  if year==`maxyear',   noid  noconstant

if _rc==0{
/*Runs k-class estimator*/
local lambda=1+e(sargandf)/e(N)
cap ivreg2 h_`yvar' (`seqexg_helm'=l(1/`maxinst').(`gmmlist') l(1/`maxtrunc').(`gmmlist_trunc'))  if year==`maxyear',  k(`lambda') nocollin coviv  noid noconstant

if _rc==0{
quietly: replace samptemp=e(sample) if year==`maxyear'
local mobs=e(N)
local obs=`obs'+`mobs'

/*Construct locals with restrictions*/
local restriction
local mresults
forvalues m=1(1)`num_seqexg'{
local restriction `restriction' & _b[h_seqexg`m']!=0
local mresults `mresults' (seqexg`m': _b[h_seqexg`m'])
}

/*Extracts results and weights them by the adjusted variance*/
if _rc==0   `restriction'  {
quietly: nlcom `mresults', post
matrix b=e(b)
matrix V=e(V)
cap matrix Num1=Num1+`mobs'*inv(V)*b'
cap matrix Num2=Num2+`mobs'^2*inv(V)
cap matrix Den1=Den1+`mobs'*inv(V)
}
}
}
}

/******************Compiles results and post them******************/
matrix est2top=inv(Den1)*Num1
matrix var2top=inv(Den1)*Num2*inv(Den1)
matrix b=est2top'
matrix V=var2top
mat colnames b = `seqexg' 
mat colnames V = `seqexg' 
mat rownames V = `seqexg' 
/*Countries in sample*/
quietly: bysort newcl: egen newsamp=max(samptemp)
quietly: replace newsamp=0 if newsamp!=1
/*Post estimation results*/
ereturn post b V, obs(`obs') depname("Dep var") esample(newsamp)

drop tsample samptemp id  h_`yvar' `seqexg_helm'  `gmmlist' `gmmlist_trunc' 
end


/*******************************************************************************************************************************/
/*******************************************************************************************************************************/
/************************************ ESTIMATION PROCEDURES AND STORING RESULTS ************************************************/
/*******************************************************************************************************************************/
/*******************************************************************************************************************************/

use "data/vdem_data.dta", clear

/* XTset */
xtset country_id year

/* Generate y-variable for GDP per capita */

gen y = gdppc_ppp_bcbt_mean_log*100

drop if year < 1890

/*******************************
Left panel: Within estimator
*******************************/

quietly: xtreg y l.y dem_ep i.year, fe r cluster(country_id)
estimates store e1
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: 0)  (lag3: 0)  (lag4: 0), post
vareffects
estimates store e1_add

quietly: xtreg y l(1/2).y dem_ep i.year, fe r cluster(country_id)
estimates store e2
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: _b[L2.y])  (lag3: 0)  (lag4: 0), post
vareffects
estimates store e2_add

quietly: xtreg y l(1/4).y dem_ep i.year, fe r cluster(country_id)
estimates store e3
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: _b[L2.y])  (lag3: _b[L3.y])  (lag4: _b[L4.y]), post
vareffects
estimates store e3_add

quietly: xtreg y l(1/8).y dem_ep i.year, fe r cluster(country_id)
estimates store e4
test l5.y l6.y l7.y l8.y
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: _b[L2.y])  (lag3: _b[L3.y])  (lag4: _b[L4.y]) (lag5: _b[L5.y]) (lag6: _b[L6.y]) (lag7: _b[L7.y]) (lag8: _b[L8.y]), post
vareffects8
estimates store e4_add

/******************************************
Right panel: GMM estimator with all moments
******************************************/
mata: mata set matafavor speed

quietly: xtabond2 y l.y dem_ep i.year,  gmmstyle(y, laglimits(2 .)) gmmstyle(dem_ep, laglimits(1 .)) ivstyle(i.year   , p) noleveleq robust nodiffsargan
estimates store e1gmm
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: 0)  (lag3: 0)  (lag4: 0), post
vareffects
estimates store e1gmm_add

quietly: xtabond2 y l(1/2).y dem_ep i.year,  gmmstyle(y, laglimits(2 .)) gmmstyle(dem_ep, laglimits(1 .)) ivstyle(i.year   , p) noleveleq robust nodiffsargan
estimates store e2gmm
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: _b[L2.y])  (lag3: 0)  (lag4: 0), post
vareffects
estimates store e2gmm_add

quietly: xtabond2 y l(1/4).y dem_ep i.year,  gmmstyle(y, laglimits(2 .)) gmmstyle(dem_ep, laglimits(1 .)) ivstyle(i.year, p) noleveleq robust nodiffsargan
estimates store e3gmm
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: _b[L2.y])  (lag3: _b[L3.y])  (lag4: _b[L4.y]), post
vareffects
estimates store e3gmm_add

quietly: xtabond2 y l(1/8).y dem_ep i.year,  gmmstyle(y, laglimits(2 .)) gmmstyle(dem_ep, laglimits(1 .)) ivstyle(i.year   , p) noleveleq robust nodiffsargan
estimates store e4gmm
test l5.y l6.y l7.y l8.y
nlcom (shortrun: _b[dem_ep ])  (lag1: _b[L.y])  (lag2: _b[L2.y])  (lag3: _b[L3.y])  (lag4: _b[L4.y]) (lag5: _b[L5.y]) (lag6: _b[L6.y]) (lag7: _b[L7.y]) (lag8: _b[L8.y]), post
vareffects8
estimates store e4gmm_add


estout e1_add e2_add e3_add e4_add e1gmm_add e2gmm_add e3gmm_add e4gmm_add using "outputs/Step3/TableMain3.tex", replace style(tex) ///
cells(b(fmt(3)) se(par fmt(2))) stats(N N_g, fmt(%7.0f %7.0f  %7.0f) ///
labels("Observations" "Countries in sample" )) ///
order(shortrun lag1 lag2 lag3 lag4 lag5 lag6 lag7 lag8 longrun effect25 persistence) ///
collabels("Model 1" "Model 2" "Model 3" "Model 4" "Model 5" "Model 6" "Model 7" "Model 8") ///
varlabels(effect25 "Effect of democracy after 25 years" shortrun  "Democracy" longrun "Long-run effect of democracy" persistence "Persistence of GDP process" lag1 "log GDP, first lag" lag2 "log GDP, second lag" lag3 "log GDP, third lag" lag4 "log GDP, fourth lag" lag5 "log GDP, fifth lag" lag6 "log GDP, sixth lag" lag7 "log GDP, seventh lag" lag8 "log GDP, eighth lag") title(Effect of Democracy on log GPD per Capita, 1789-2014)


